Skyfire, Do you remember if that doc was online?
I searched "site:us.fulbrightonline.org additional funding" and couldn't really find any specifics other than this statement: The allowance provides some funding for research, books, and/or supplies. Grantees with projects that require extensive research support, in-country travel, study materials, or equipment should explore additional funding from other sources to supplement the Fulbright funding
Edit: I found the 2011 brochure that states:
Funds from Other Sources. Funds from other scholarships, fellowships, or grants in dollars or foreign currencies received concurrently with a Fulbright grant will be deducted if they duplicate benefits under the Fulbright grant. But, if such grants are for assistance in meeting family expenses of grantees or other expenses not covered by the Fulbright grant, no deduction will be made. Grantees may not accept remunerative work abroad during the period of the grant without prior approval of the Fulbright Commission or U.S. Embassy in the host country.
It seems vague at best. Seems to indicate they want to know what other funds you have so they can make final approval